The principle of three-dimensional printing and imaging

Stereoscopic printing is based on the physiological characteristics of the human eye to form a three-dimensional sensation and the optical principle of the refracting image of the grating plate. By using a grating plate, the planar two-dimensional image scene has a three-dimensional effect. The following is a brief introduction to the principle of three-dimensional printing imaging.

1. Physiological characteristics of the human eye The object is in a three-dimensional space. The visual system can present a three-dimensional image of a binary image formed by a target object at a different distance and depth on the retina, which is called a stereoscopic visual sense. From the physiological point of view, there are many reasons for the formation of stereoscopic vision, including physical and psychological. From the analysis of imaging theory related to three-dimensional printing, the physiological formation of stereoscopic vision can be regarded as the two processes of determining the fixation point first by convergence and then performing accurate depth and position determination by the binocular parallax.

1 When the two eyes stare at an object at the same time, if the object is far away, the eyes of the two eyes are basically parallel. When the object approaches, both eyes rotate inwards, and the line of sight intersects at the object. This action of both eyes is called convergence. The convergence has a direct effect on the formation of a sense of depth. The depth sensation caused by the convergence is effective within 20m from a short distance, and its effect is significantly reduced at a long distance.

2 The binocular parallax is shown in Fig. 1. There is a certain distance between the pupils of the two eyes in the horizontal direction (eye distance a). When viewing the object, a certain angle is formed between the object and the object, so the object is on the retinas of the left and right eyes. Imaging is not exactly the same. This difference is called binocular parallax.

When looking at point F, the retina f and f' are imaged at the left and right eyes, respectively. However, the point E farther than F and the point G closer than F are imaged at positions e, e', and g, g', respectively. Obviously, the geometrical positions of E, F, and G on the retinas of the left and right eyes are different, so that the different images obtained by integrating the left and right eyes of the brain produces a sense of depth. In general, α, β, γ represent convergence angles (angles of convergence), and (β-α), (γ-α) represent the corresponding parallax angles.

The images formed by the left and right eyes of the object can be well integrated into one within a certain parallax range, and constitute the depth and position information.

At this time, the perception of depth and stereoscopic vision are produced. The range of perceived depth of binocular parallax is basically determined by the fusion of the two eyes, and is not very wide. However, binocular vision has very high precision in the resolution of depth differences within the effective range.

Due to the combined effect of convergence and binocular parallax, a correct stereoscopic vision can be obtained within a wide range.

3 Permissible range of binocular disparity Based on the function and characteristics of binocular parallax, the image difference between the two eyes can be maintained within 5%-10%, as follows: (a) Image size difference: Geometry is within 5%: The difference is 1 -2% will cause eye fatigue; 3-4% parallax will cause obstacles; 5% or more can not establish a stereoscopic sense.

For general graphics, the difference can be kept at 10-15%.

(b) Brightness difference: within 30% (c) Chromaticity difference: ±15 nm (d) Resolution difference: within 10% (up to 30% for low-resolution images) 4 Regulating action of the lens produces stereoscopic vision The reason for this is that in addition to convergence and binocular parallax, the adjustment of the lens also plays a role. By varying the thickness of the lens, objects at different distances can be imaged on the retina, giving a certain sense of depth.

But this distance is not very large, generally limited to 2-3 meters.

2. Imaging principle of the lenticular lens grating plate The lenticular lens grating plate has many small cylindrical lens element planes with the same structural parameters and performance. The one side is flat, and the other side is a surface with periodic fluctuations, as shown in Fig.3. . In the arrangement direction, each cylindrical lens element is equivalent to a converging lens, which functions as focusing and focusing, and the plane of the lenticular lens grating plane is a focal plane.

This feature makes it have "compression" and "isolation" effects on the image.

1 Analysis of the geometrical light path of a cylindrical lens element Zooming in and viewing The cylindrical lens grating element that composes the cylindrical lens can not be neglected because its thickness is larger than its radius of curvature. Therefore, it must be considered as a thick lens for optical analysis and it belongs to a thick lens. The plano-convex lens, as shown in Figure 4.

Thick lenses can be treated as being composed of two spherical refractive surfaces separated by a distance d (ie, OO'). After a tedious algebraic calculus, the following set of formulas can be obtained: (1) where the object distance s 0 and the image distance s 1 are measured from the first principal plane H 1 and the second principal plane H 2 , respectively, and the focal length f is also It is relative to the main plane H 1 . That is, s 0 refers to the distance from the object point to the first principal plane H1; s 1 refers to the distance from the image point to the second principal plane H2; f is the distance from the focal point to the first principal plane; h 1 refers to the first optical surface to The distance from the first principal plane (Oh 1); h 2 is the distance from the second optical plane to the second principal plane (Oh 2); R 1 is the radius of curvature of the first optical plane; R 2 is the second optical plane Radius of curvature.

Due to R 1 ∞, the formula set (1) can be simplified and calculated as follows: (2) According to the formula set (2), it can be known that when the object distance s 0 and the focal length f are known, the image distance s 1 and the focal length f and the refractive index of the lens can be obtained. n relates to the radius of curvature R2.

In a three-dimensional print, the grating plate is attached to the image, and the plane of the grating plate is the focal plane, ie the image is located on the focal plane (fd). Because of this particularity, the cylindrical lens elements composing the cylindrical lens grating plate have a special optical property - any certain cylindrical lens on the image surface is refracted into a parallel beam.

The optical path diagram of the cylindrical lens element is shown in Figure 5.

The point C in the figure is the node of the cylindrical lens. The distance from the first optical surface to the point C is q. The coordinate system O y is taken and the origin O is on the optical axis. For the y0 point, a very thin beam parallel to the optical axis after the cylindrical mirror carries the corresponding information transmission with a transmission direction angle of 0°. For any y point, after the cylindrical lens into a very fine parallel beam, carrying the corresponding information transmission, the value of its transmission direction angle. Because, therefore: (3) And because, into (3): (4) It can be seen that the light emitted from different positions on the O y plane is refracted by the lens and becomes a very fine parallel beam, and will be transmitted in different directions. And each of these beams carries its own information. Because the direction angles of the beams formed after refraction at different points are different, the cylindrical lens functions as an image splitter.

From Equation (4), we can know that the transmission direction angle of the light is related to the radius of curvature R 2 , the refractive index n and the position of the y point. For a particular grating plate (ie, R 2 and n are known), we can determine the direction of light transmission at a particular point and perform microscopic optical path analysis on the grating plate.

The imaging process of the 2-pole lens grating plate The cylindrical lens grating plate is a collection of many cylindrical lens elements. The optical principle is the arrangement of miniature unidirectional magnifying glass. Its optical function is to compress and amplify the planar image in one direction, so the cylindrical lens grating plate Can accommodate a large number of flat images and maintain the integrity of the plane image.

It will be compressed into a striped planar image, arranged in the right and left order at the corresponding position on the focal plane of the lens. The lenticular lens grating combines the image information carried by the very small light beams of each cylindrical lens element, and images the left and right eye retinas respectively, and forms a corresponding stereoscopic image through the central nervous system. Through binocular movement, the information carried by different light beams is obtained, so that a three-dimensional image with a very rich amount of information is obtained, as shown in FIG. 6 .

3. Reasons for Stereoscopic Depth Due to Three-Dimensional Prints As mentioned before, the main reason for the formation of three-dimensionality is due to the binocular parallax of people. When the brain synthesizes the image information obtained by the two eyes, one of the most important factors is the incident direction of the object's light. The orientation and distance of the object point can be determined according to the directions of light emitted or reflected by each object point. .

Light emitted from point E on plane M enters into left and right eyes respectively, and a middle scene is formed at this time.

As described above, as long as a set of left and right scene images of a scene can be recorded and left and right eyes respectively see only the corresponding parts in the corresponding left and right images, the eye adjusts the focusing angle due to the relative parallax between the left and right images. Just like the state of the simulation to watch real scenery, it produces a real stereo feeling.